光イオン化法で生成したYb+のRFイオントラップ

Title Trapping of Yb+ Loaded through Photoionization in RF Ion_{Trap( Dissertation_全文 )}

Author(s) Onoda, Yugo

Citation Kyoto University (京都大学)

Issue Date 2012-01-23

URL http://dx.doi.org/10.14989/doctor.k16503

Right

Type Thesis or Dissertation

Textversion author

Trapping of Yb

Loaded through Photoionization

in RF Ion Trap

(

光イオン化法で生成した

Yb

_の

_RF

_{イオントラップ}

₎

Yugo ONODA

2011

i

Abstract

In this thesis, we present our study on loading of Yb+ _{ions produced by photoionization}

into a radio frequency (RF) trap. Yb+ _{is one of the attractive ion species for use in}

opti-cal frequency standards and quantum information processing. Photoionization is recently applied as a method of loading of ions into the ion trap, because it has some advantages such as high eciency and isotope-selectivity. Photoionization loading of Yb+ _{ions has}

been already used in several studies. However, a detailed investigation of the loading has not been conducted so far. We measure the loading rate by using the electric resonance detection of the secular motion of the trapped Yb+ _{ions. They are cooled with a helium}

buer gas. Unlike the measurement using the ions trapped with help of laser cooling, we remove the eect of the cooling eciency from the loading rate owing to high eciency of buer-gas cooling. From the electric resonance signal, one can estimate the number of trapped ions. We can determine the loading cross section by using the estimated ion number. The loading cross section enables us to compare the results with those obtained in other systems.

Before we measure the loading rate, we improve the method of number estimation from the electric resonance signal, and we prepare light sources for photoionization. As the improvement of the number estimation, we decrease the uncertainty in the number esti-mation to be approximately 10% even in the presence of anharmonicity, when the relative signal height is smaller than 0.3. This is essential because the anharmonicity accompanies the usual trap design and causes a hysteresis in the electric resonance signal.

For the light source, we obtain the results not only useful for our investigation of the loading rate but also applicable to other studies using various atoms and ions. We need to develop a single-frequency and continuously frequency tunable light source at 399 nm, with which the 1_S

0−1P1 transition in Yb atoms is driven as the rst-excitation

ii Abstract isotope-selective loading. The radiation that we rst developed is second-harmonics of a continuous-wave (CW) titanium-sapphire-laser radiation. In order to enhance the con-version eciency in second harmonic generation of the CW laser that usually has small output power, a nonlinear crystal that generates second harmonics is placed in the ex-ternal cavity. When an antireection-coated normal-cut nonlinear crystal is used in an external cavity, a small residual reection at the crystal facets causes a round-trip loss and prevents the realization of a large fundamental enhancement. This problem is eliminated when the reected beams at the crystal facets are subject to constructive interference. We demonstrate that the temperature tuning of a β-BaB2O4 crystal is eective to realize

constructive interference at any wavelength. The radiation that we secondly developed is that of an extended-cavity laser diode (ECLD) using a high-power ultraviolet diode chip that is very recently available. We achieve a single-frequency oscillation even at the maximum operation power of the chip, when the cavity length of the ECLD is shortened. A precise frequency tuning is required for the isotope-selective loading using the isotope shifts in the transition used as the rst excitation of photoionization. We demonstrate a simple method to detect minor isotope lines in a saturated absorption spectrum by ab-sorption ltering of major isotope lines. We investigate this method for the spectroscopy of the 1_S

0 −1P1 transition in Yb by controlling the density of Yb atoms by varying the

discharge current of a hollow cathode lamp. We selectively detect the lines of the useful isotope of 171 and of the isotope of the smallest natural abundance of 168.

As the main study of this thesis, we investigate the photoionization loading into a RF trap, in particular, the loading rate by two-color and one-color photoionizations and the eect of the charge exchange collision on the isotope-selective loading. In two-color pho-toionization, where the rst-excitation laser drives the1_S

0−1P1 transition in the Yb atom

and the second one ionizes the atom from the 1_P

1 state, we measure the dependence of

the second-excitation wavelength. That the loading rate is at its highest by the excita-tion of the ionizaexcita-tion potential. A similar loading rate is observed at the second-laser wavelength around 369.5 nm, which is the wavelength for the cooling transition of Yb+_.

Thus we quantitatively conrm that the cooling laser of Yb+ _{is a good substitute for the}

second-excitation laser. The excitation of the Yb atoms in the Rydberg states is detected by the enhancement of the loading rate. By irradiation with only the rst-excitation laser, i.e., in one-color excitation, Yb+ _{is produced at a rate three orders of magnitude}

iii smaller than that in two-color excitation of the ionization potential, as the non-resonant two-photon absorption from the 1_P

1 state is the dominant process. Using the number

estimation method that we improve, we determine the number loading rate. And then, we estimate the loading cross section to be 40(15) Mb for the two-color excitation of the ionization potential. Because we improve the uncertainty in the number estimation, the uncertainty in the loading cross section is limited by those in the estimations of other parameters such as the density of Yb atoms. Because the ionization region is smaller than the trap region and an ecient buer-gas cooling is combined, our method could be a useful one for measurement of the rate and cross section of photoionization. We also measure the charge-exchange rate between Yb+ _{and Yb atoms from the oven by using}

two enriched isotopes. We discuss its eect on isotope-selective photoionization loading by using the rates of the photoionization loading and the charge exchange that we estimate. We conclude that the charge exchange is a signicant factor in limiting the number of target isotope ions that are purely isotope-selectively loaded, only for the target isotope of its abundance smaller than 0.1%, i.e., the rarest isotope of 168 in the natural isotope mixture, in our photoionization scheme of Yb. The loading duration is required to be much smaller than the inverse of the charge exchange rate.

v

Contents

1.2 Purpose of present study and outline of this thesis . . . 3

Chapter 2 Principle of RF Ion Traps 7 2.1 RF Ion Trap . . . 7

2.2 Electric Resonance Detection Method . . . 9

2.2.1 Anharmonic oscillation . . . 10

2.2.2 Experimental setup . . . 13

2.2.3 Results . . . 13

2.3 Collective oscillation . . . 14

2.4 Summary . . . 15

Chapter 3 Light Sources for Photoionization of Yb 17 3.1 Second Harmonic Generation of Titanium Sapphire Laser with External Cavity Technique . . . 18

3.1.1 Eect of round-trip loss on enhancement factor . . . 19

3.1.2 Experimental setup . . . 22

3.1.3 Results and analysis . . . 23

3.2 External Cavity Laser Diode . . . 29

3.3 Saturated Absorption Spectroscopy of Yb Atoms in Hollow Cathode Lamp 32 3.3.1 Principle of selective detection of minor isotope lines . . . 32

vi Contents

3.3.2 Experimental setup and results . . . 34

3.4 Summary . . . 36

Chapter 4 Photoionization loading of Ytterbium ions 37 4.1 Principle of Measurement . . . 38

4.2 Experimental setup . . . 39

4.2.1 Measurement procedure of loading rate . . . 39

4.3 Two-color photoionization . . . 40

4.3.1 Dependance on second-excitation wavelength . . . 40

4.3.2 Determination of loading cross section . . . 43

4.3.3 Enhancement of loading rate by excitation to Rydberg state . . . . 44

4.4 One-color Photoionization . . . 46

4.5 Measurement of Charge Exchange Rate . . . 48

4.5.1 Eect on isotope-selective photoionization loading . . . 50

4.6 Summary . . . 54

Chapter 5 Summaries 57 5.1 Summary of this study . . . 57

5.2 Future prospect . . . 60

Bibliography 61

Appendix A BBO Crystal 67

Appendix B Clausius-Clapeyron Equation 68

Acknowledgments 70

1

Chapter 1

Introduction

1.1 Background

Ion trap technique is one of the methods to provide reference frequencies used in optical frequency standards. Connement of atoms within the order of the wavelength, i.e., the Lamb-Dicke regime, eliminates the rst-order Doppler shift. Applying laser cooling to the trapped ions enables us to achieve the Lamb-Dicke connement of the optical wave-length. A fractional frequency instability of the optical frequency standard is expected to be improved by a factor of 104_{, from that of the frequency standard at present, dened in}

microwave by the transition between the hyperne structures of the ground state in ce-sium. In single-ion optical clocks, an uncertainty of the order of 10−18 _{in the frequency is} predicted and has been demonstrated very recently [1], because they are insensitive to the perturbations which shift the transition frequencies. Singly ionized ytterbium ion (Yb+₎

is one of the suitable ion species for use in optical frequency standards [2, 3], and is also applied to a qubit in quantum information processing [4]. Yb+ _{has energy levels like}

alkali-metal atoms. The partial energy diagram is shown in Fig. 1.1. The transition used for laser cooling and optical detection is the2_S

1/22P1/2 transition at 370 nm. In order to

continue the cooling cycle, the2_D

3/23D[3/2]1/2 transition at 935 nm is driven to deplete

the 2_D

3/2 metastable state. The odd isotopes of Yb+ have magnetic sublevels of mF = 0

which have no rst-order Zeeman shift. Therefore, the transitions between mF = 0 and

m′_F = 0are suitable as clock transitions. The odd isotopes have an disadvantage that they have hyperne structures and a scheme of laser cooling is more complicated than that for

2 Chapter 1 Introduction

2

_S

_1/2

2

_P

_1/2

Cooling

370 nm

2

_D

_3/2

3

_D

_[3/2]

935 nm

435 nm

Fig. 1.1 Partial energy diagram of Yb+_.

the even isotopes that have no hyperne structures. In the odd isotopes of Yb+_, 171_Yb+

is the most attractive because it has relatively simple hyperne structures because of the nuclear spin of 1/2. The natural abundances of the stable isotopes of Yb are shown in Table 1.1 [5].

In the ion trap technique, loading ions into the trap is required as the rst step. The trapped ions are usually loaded through ionization of neutral atoms inside the trap region. Electron-impact ionization is conventionally used for this purpose. Recently, photoioniza-tion has been widely used because it oers the following advantages [610]: (i) It is free from electrons, which stick on insulators supporting the trap electrodes and thus generate stray DC elds that enlarge the micromotion. (ii) It has higher ionization eciency than electron impact ionization. This enables us to decrease the density of neutral atoms to be ionized, thus, suppressing the generation of a patch potential between the electrode surface and the neutral atoms deposited on it. This patch potential also enlarges the mi-cromotion. (iii) Photoionization oers isotope-selective loading through the isotope shifts in the intermediate states. (iv) Finally, it also leads to uorescence of trapped ions during the loading process. This enables us to load ions one by one.

In the photoionization loading of Yb+_{, the} 1_S

01P1 transition at 399 nm in Yb atoms

1.2 Purpose of present study and outline of this thesis 3

Table. 1.1 Natural abundances of stable isotopes of Yb atoms.

Mass number Natural abundance / %

168 0.1 170 3 171 14 172 22 173 16 174 32 176 13

the photoionization conducted in this thesis is shown in Fig. 1.2. In the rst report of the photoionization loading of Yb+ _{[11], only the radiation at 399 nm was used. We refer to}

this photoionization as one-color photoionization in this thesis. Subsequently, two-color photoionization was reported, where simultaneous irradiation with light at 370 nm, which drives the2_S

1/22P1/2 cooling transition in Yb+, increased loading eciency by a factor

of 10 [10]. Although two-color photoionization has been used in subsequent research and a loading cross section was roughly estimated [12], the photoionization loading of Yb+

has not been quantitatively investigated thus far. The purpose of this study is to conduct quantitative measurements of the loading rate of Yb+_{loaded through photoionization. We}

compare various loading conditions, and discuss the ionization scheme of one-color pho-toionization and the eect of the charge exchange collision on isotope-selective loading, which have not been claried so far.

1.2 Purpose of present study and outline of this thesis

In order to conduct quantitative measurement of the loading rate of Yb+ _produced

by photoionization, we use the electric resonance detection of the secular motion of the trapped ions. For this purpose, we stored a large number of ions with buer-gas cooling. In the electric resonance detection method, the excitation of the secular motion of the trapped ions is detected by using a probe radio frequency (RF) eld. This method is advantageous for quantitative investigations of the loading rate in two ways: (i) One

4 Chapter 1 Introduction

Fig. 1.2 Partial energy level of neutral Yb for photoionization scheme. I.P., ionization potential.

can determine the number of trapped ions from the electric resonance signal [13], which enables us to estimate the loading cross section. In a previous study [14], the electric resonance was used for measurement of electron-impact ionization cross sections of helium in a somewhat dierent way from ours; in that study, the ion density was estimated from the shift in the secular frequency by the space charge of trapped ions. (ii) No radiation is required for detecting trapped ions. The latter advantage is particularly useful in the case of Yb+_{. When Yb}+ _{is irradiated with resonant light in the presence of buer gases,}

Yb+ is pumped to the 2F7/2 metastable state [15, 16] and has a loss in the excited state

because of molecular formation with background gases [17]. In ultra high vacuum, these problems are eliminated. However, laser cooling is required to observe trapped Yb+_{. The}

uorescence intensity is not only proportional to the number of Yb+ _{ions but also depends}

on the translational energy of Yb+_{, which is a function of laser detuning and of the total}

number of trapped ions. Even when the loading rate can be determined from the step increase in the uorescence caused by one-by-one loading, it may be inuenced by the cooling eciency, which depends on the detuning and intensity of the cooling laser.

We also investigate the charge exchange process between the trapped Yb+ _{ions and the}

Yb atoms from the oven. This is one of the possible causes that limit the number of ions that have been purely isotope-selective loaded [8]. We discuss the eect of the charge exchange collision using the measured rates of loading and charge exchange. Charge exchange cross section or rate coecients of the collisions between Yb+ _{and Yb have been}

1.2 Purpose of present study and outline of this thesis 5 theoretically estimated in a large energy range [18] and experimentally determined in the semiclassical regime [19]. Measurement of a charge exchange cross section using electric resonance detection was reported in [20].

The following is the outline of this thesis. Before we investigate the photoionization loading of Yb+ _{in detail, we improve the number estimation using the electric resonance}

detection and prepare light sources to be used for photoionization. Chapter 2

In this chapter, we rst describe the principles of the RF trap and the electric resonance detection method. One can determine the number of trapped ions by using the electric resonance signal. The product of the signal height and width is in proportion to the ion number. However, when the trap potential has an anharmonicity, which accompanies the trap ordinarily designed, the signal is distorted and an uncertainty in the number estima-tion is much increased. We found a method to avoid the problem of the anharmonicity in order to compare the relative loading rate with various conditions. Then, we decrease the uncertainty in the number estimation even in presence of the anharmonicity. This enables us to determine the number loading rate required for estimation of the loading cross section. We shortly describe the collective oscillation of trapped ions. This is used for measurement of the charge exchange rate.

Chapter 3

In this chapter, we describe the light sources that we developed for photoionization of Yb atoms. In order to photoionize Yb atoms, two light sources are required, i.e., one is used for driving the1_S

01P1 transition at 399 nm. the other is for ionizing the Yb atoms in the 1_P

1 state. A continuous-wave (CW), single-frequency, and continuous frequency-tunable

laser is desirable as a light source for driving the 1_S

01P1 transition. This enables us to

conduct isotope-selective loading by using the isotope shift in the transition. In the course of development of the light sources, we obtain three results that can be widely applied to other systems. First, we found a method to maximize the fundamental enhancement factor of an external cavity, where a nonlinear crystal generating second-harmonics is placed, when a loss by a small residual reection at anti-reection coated facet is not negligible small. The external cavity technique is widely used to increase conversion eciency when one conducts second-harmonic generation (SHG) of a CW laser which is

6 Chapter 1 Introduction usually low output power. Second, we found how to realize single-frequency oscillation in an extended-cavity laser diode (ECLD) using a high-power ultra violet diode chip recently developed, even when the diode chip is operated at the maximum output. Third, we found a simple method to detect minor isotope lines in a saturated absorption (SA) spectrum by absorption ltering of major isotope lines. SA is one of the technique used in Doppler-free high-resolution spectroscopy and is applied for the detection of the transitions in atoms and molecules used to obtain reference frequencies.

Chapter 4

This chapter is devoted to describe the results of the main purpose of this thesis de-scribed above. We compare the loading rate with various ionization condition, i.e., the dependence of the second-excitation wavelength, the ionization through the Rydberg state, and investigations to clarify the mechanism of one-color photoionization. We measure the loading cross section by using the number of trapped ions estimated from the electric resonance signal by using the improved method described in Chap. 2. We measure charge exchange rate by using enriched 171_{Yb and} 174_{Yb as a source of Yb atoms. We discuss}

the eect of the charge exchange collision on isotope-selective photoionization loading. Chapter 5

7

Chapter 2

Principle of RF Ion Traps

In this chapter, we summarize the principle of trapping of charged particles in the RF trap. Then, we describe the method of detecting the trapped charged particles by the electric resonance method. Using the electric resonance signal, one can determine the number of trapped charged particles. In the trap ordinarily designed, the motions of the trapped charged particles have anharmonicity. The anharmonicity distorts the signals and degrades the uncertainty in the number estimation. We develop the number estimation method to be useful even in the presence of anharmonicity. We demonstrate the improved number estimation method with an RF trap used for investigations of photoionization loading. We determine the conversion factor from the relative signal height of the electric resonance signal to the ion number. This conversion factor is required for conversion of the relative loading rate to the number loading rate, from which the loading cross section is estimated. Finally, we briey describe the collective oscillation, used in the measurement of the charge exchange rate described in Sec. 4.5.

2.1 RF Ion Trap

We use a conventional RF ion trap. The electrodes of the RF trap are com-posed of two endcap and one ring electrode which surfaces are hyperboraid of revolution as show in Fig. 2.1. An RF driving voltage Vaccos Ωt on which a dc electric voltage Vdc

is superimposed is applied between the endcap and the ring electrodes. The trajectory of a trapped ion is governed by the Mathieu equation: d2_u

8 Chapter 2 Principle of RF Ion Traps 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 −0.1 −0.2 −0.3 −0.4 −0.5 −0.6 −0.7 0.2 0.1

Fig. 2.1 Stability diagram of Mathieu equation. The parameters of az and qz in

shaded area satisfy the condition where the charged particle is stably conned in three dimensions.

(i = r, z), where Mathieu parameters ai and qi are respectively deduced to be

az =−2ar = −8eV dc mr₀2Ω2 (2.1) and qz =−2qr = 4eVac mr2 0Ω2 , (2.2)

where e and m are respectively the charge and mass of the trapped ion. The relationship r₀2 = 2z₀2is selected as a conventional trap design, where r0 is the minimum inner radius of

the ring electrode and z0 is the minimum half distance between the two endcap electrodes.

The stability diagram of the Mathieu parameters az and qz are show in Fig. 2.1. The

secular frequencies of trapped ions, ωi, are given by

ωi =

βiΩ

2.2 Electric Resonance Detection Method 9 where βi ≈ (ai + q2i/2)1/2. The depthes of the pseudopotential well in the r- and z-direction, eDr and eDz are respectively given by

eDr = mΩ2 8 β 2 rr 2 0 (2.4) and eDz = mΩ2 8 β 2 zz02. (2.5)

2.2 Electric Resonance Detection Method

The secular motion of the trapped ions is excited by a probe RF electric eld, when the frequency of the probe is in agreement with the secular frequency. One can determine the absolute or relative number of trapped ions from this resonance signal. The block diagram of the electric resonance detection is shown in Fig. 2.2. The probe RF current source, composed of an RF voltage source with an output of V0cos ωt and

a high resistance Rf, is connected between the endcap electrodes to excite the secular

motion of the trapped ions in the axial- or z-direction. The series resonance circuit resonant at Ω and the parallel resonance circuit resonant at ω are also connected between the endcap electrodes to x the electrodes to the same electric potential at Ω and DC, respectively. The amplitude at ω between the endcap electrodes is measured using the following electronics composed of a high-input-impedance amplier, a lter to remove the component at Ω, and a rectier.

To detect the resonance signal, the probe frequency or the secular frequency of trapped ions are swept. By the probe-frequency sweep, one can determine the absolute number of trapped ions N from the following equation [13]:

N = Ymax∆ω ( 4mz₀2 Γ2_e2 ) ( 1 Rf + G0 ) 1 b , (2.6)

where the relative signal height Ymax is dened as Ymax = (V10 − V1)/V10; here V10 and

V1 are the values of the voltage between the parallel resonance circuit at ω when the

ions are removed and trapped, respectively. ∆ω is the full width at half maximum of the relative absorption signal in angular frequency, b = [(2 − 1.5Ymax)/(2− 0.5Ymax)]1/2, Γ is

10 Chapter 2 Principle of RF Ion Traps and G0 is the conductance of the parallel resonance circuit without trapped ions. The

electric resonance detection can be applied to any type of traps in order to estimate N, although a large number of trapped ions, e.g., 104 _{ions in our setup, is required in the case}

of the trap related to the RF trap. The value of Γ depends on the electrode shape and the ratio between the translational energy of trapped ions and the trap potential [13].

To sweep the secular frequency of trapped ions, the sweep of Vdc is widely used because

of its convenience. The equation to determine N from the signal detected by the Vdc

-sweep is not known. However, one can employ the signal obtained by the Vdc-sweep for

comparing the relative number of trapped ions [21].

2.2.1 Anharmonic oscillation

In the usual trap setup, the signal is distorted by an anharmonicity, which causes a hysteresis and a shift of the resonance frequency. Figure 2.3 shows a sample of the an-harmonic electric resonance signal detected with our setup through the probe-frequency

Sweep of probe frequency

Filter Rectifier

Amp.

noise level

Fig. 2.2 Schematic diagram of the experimental setup for electric resonance detec-tion of trapped ions in radiofrequency (RF) trap. When the secular frequency of

trapped ions ωz equals the probe frequency ω, the trapped ions absorb the probe

energy and an absorption signal is observed. The series resonance circuit removes the component at the frequency Ω of the RF driving voltage.

2.2 Electric Resonance Detection Method 11 52 950 53 000 53 050 53 100 53 150 52 900

Probe frequency / Hz

Re

la

ti

ve

s

igna

l he

ight

Fig. 2.3 Sample of electric resonance signal with anharmonicity detected by probe-frequency sweep. We show a relative signal height Y , i.e., dierence in the parallel resonance curve in the cases with and without trapped ions. The arrows indicate the scanning directions of the probe frequency. The parameters of the electric resonance detection are given in Sec. 2.2.1. The solid line denotes a tting curve expressed by Eq. (2.7). The best tting values of ∆ω and ξ are shown in the gure.

sweep with two sweep directions, i.e., from low to high frequency and its reverse direction. The anharmonicity is caused by the fact that the electrodes are not innitely extended hyperboloids of revolution [22] and is modied by the space charge of trapped ions when the number of trapped ions is large [23]. When the trap electrodes are symmetric along the trap axis and the plane at z = 0, the truncated trap electrode generates an octupole potential that induces the anharmonicity. The axial or radial secular frequency is pro-portional to the square of the amplitude of the secular motion, which is expressed by a Dung equation. Even when the signal has this anharmonicity, the signal height de-tected by the sweep direction of the larger signal is the same as that in the case of no anharmonicity [22]. In the case of no anharmonicity, increase in the signal height grows smaller as the number of trapped ions increases, while the product of the signal height and width still proportionally increases as shown in Eq. (2.6). However, when the number of trapped ions is small and Ymax is smaller than 0.2, Ymax is proportional to the number

12 Chapter 2 Principle of RF Ion Traps ion number is approximately 10%. This is proved by comparison between Ymax and the

product of Ymax and ∆ω, performed by numerical calculation, irrespective of the probe

frequency sweep or Vdc sweep [13, 21, 24] . Therefore, when Ymax is smaller than 0.3, it

is possible to compare the relative number of trapped ions using only Ymax detected by

the sweep direction of the larger signal even in the presence of the anharmonicity. This characteristic enables us to determine the relative loading rate by using Ymax, because

the relative loading rate is estimated at the start of loading where the number of ions is approximately zero, as we later describe in Sec. 4.1.

If we can measure the conversion factor from the Ymax detected by Vdc sweep to N

even in the presence of anharmonicity, we will be able to convert the relative loading rate to the number loading rate, from which we can estimate the loading cross section. In the case of no anharmonicity, the measurement of the conversion factor is easily ac-complished by detecting the signals to the same number of ions both by the Vdc-sweep

and the probe-frequency sweep. We determine N from the signal by the probe-frequency sweep by using Eq. (2.6), and thus obtain the conversion factor N/Ymax. However, when

an anharmonicity is present, the signal width of the sweep direction of the larger signal is wider than ∆ω. Therefore, we need to estimate the value of ∆ω from the anharmonic signal in order to determine N using Eq. (2.6).

With the above mentioned anharmonicity, the secular frequency varies in proportion to the square of the amplitude of the secular motion [22]. In the electric resonance signal, the current induced by the secular motion can be detected. The amplitude of the signal is proportional to the velocity and, hence, to the amplitude of the secular motion. Therefore, the shift of the secular frequency can be described to be in proportion to the square of the relative signal height Y of the electric resonance signal, i.e., ωz(Y ) = (1 + αY2)ωz0, as

we introduce a factor of proportionality α, where ωz0 is the secular frequency in the

ab-sence of anharmonicity. The shape of the electric resonance signal by the probe-frequency sweep can be approximately expressed as a Lorentz prole in the case of no anharmonicity because the quality factor of the signal is high. Subsequently, we approximate the pro-le of the anharmonic signal by introducing the dependence on the square of the signal amplitude to the secular frequency;

Y Ymax = [ 1 + 4 ( ω− ωz0 ∆ω − ξ Y2 Y2 max )2]−1 , (2.7)

2.2 Electric Resonance Detection Method 13 where ξ is a dimensionless parameter introduced to express the dependence of ωz on the square of the signal amplitude. The relation between α and ξ is shown as ξ = α(ωz0/∆ω)Y

2

max. By tting the electric resonance signals detected by the two sweep

directions to Eq. (2.7), we estimate the value of ∆ω and then determine N from Eq. (2.6) even in presence of the anharmonicity.

We demonstrate the improved number estimation method using an RF ion trap used for investigations of photoionization loading, and determined the conversion factor N/Ymax.

2.2.2 Experimental setup

The ion trap used has r0 of 17.0 mm and z0 of 12.0 mm. The AC driving voltage has

an amplitude of Vac = 250 V and a frequency of Ω/2π = 300 kHz. The axial secular

frequency of trapped 174_Yb+_{, ω}

z/2π, is approximately 53 kHz. The trap potential in z-and r-direction are 15 eV z-and 11 eV, respectively, calculated from Eqs. (2.4) z-and (2.5). One of the endcap electrodes is made of a mesh. The ring electrode has four holes in the z = 0 plain, arranged at 90 degrees to each other. These allow us to introduce laser beams. Two ovens are used for producing Yb vapor; one oven contains an enriched isotope174_{Yb while}

the other contains171_{Yb. The abundances of the enriched 174 and 171 sources are 98.97%}

and 90.6%, respectively. We use the 174_{Yb oven except that we notify the use of} 171_Yb

oven. The background pressure of the vacuum chamber where the ion trap apparatus is placed is 3 × 10−7_{Pa. We introduce helium gas having a pressure of 5.3 × 10}−5_{Pa as a} buer gas for cooling of trapped ions. The lifetime of trapped 174_Yb+ _{ions is over 10}4_s.

The parameters of the electric resonance detection are as follows: V0 = 3 mV, Rf =

2 MΩ, and G0 = 3× 10−7S. Because the translational energy of the buer gas cooled

Yb+ _{ions, which is supposed to be approximately 1200 K [25], is much smaller than the}

trap potential and the ions are located around the center of the trap, Γ is approximately 1 [13]. The sweep rate of Vdc and probe frequency ω/2π are set to be 50 mV/s and 50 Hz/s,

respectively. These are suciently slow in order to prevent ringing of the signal [24].

2.2.3 Results

We determine the conversion factor N/Ymax, as described in Sec. 2.2, for Ymax ≤ 0.3.

14 Chapter 2 Principle of RF Ion Traps respectively, by tting Eq. (2.7) to the signals for probe-frequency sweep in two directions. Accordingly, we estimate N/Ymax for eight samples between Ymax =0.1 and 0.3 as shown

in Fig.2.4 , and average these values to determine N/Ymax to be 2.7(3) × 105. The

uncer-tainty is caused by the tting error and the small deviation of Ymax from the proportional

increase to N as described in Sec. 2.2.1.

2.3 Collective oscillation

When the ions having similar, but not the same, charge-to-mass ratios are simultane-ously trapped, a collective oscillation is observed, i.e., the ion cloud moves as one parti-cle [26]. This results in a single resonance in the electric resonance signal; the resonance frequency depends on the ratio of the number of each ion. In the case of two singly charged ion species, the resonance frequency corresponds to that of the equivalent mass m0 = [(N1m1+ N2m2)m1m2/(N1m2+ N2m1)]1/2 [27] . One can estimate the ratio of the

two ion species from the resonance frequency. If we prepare two pure isotopes of atoms,

9 8 7 6 5 4 3 2 1 0 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Fig. 2.4 Dependence of conversion factor N/Ymax on Ymax. Since the number of

trapped ions N is proportional to Ymax when Ymax ≤ 0.3, N/Ymax is approximately

constant. We determine N/Ymaxfrom eight samples as indicated by dotted line circle,

2.4 Summary 15 trap the ions of one of the two isotopes, and collide them with the other isotope of atoms, we can determine the charge exchange rate from a temporal change in the resonance fre-quency. We will describe the measurement of the charge exchange rate between Yb+ _and

Yb atoms in Sec. 4.5.

2.4 Summary

In this chapter, we summarize the principles of the techniques used in this work, i.e., the RF trap and the electric resonance detection. In the electric resonance detection, one detects the frequency of the secular motion of trapped ions. We focus on two character-istics of the secular motion; one is the anharmonic oscillation, the other is the collective oscillation. The anharmonicity accompanies the trap ordinarily designed, and degrades the uncertainty in estimation of the number of trapped ions using the electric resonance signal. We develop the number estimation method in order to improve the uncertainty even in the presence of anharmonicity. We determine the conversion factor N/Ymax with

an uncertainty of 10% when Ymax ≤ 0.3. This enables us to convert to the Ymax loading

rate to the number loading rate used for determination of the loading cross section. The collective oscillation is used for measurement of the ratio of the isotopes of trapped ions. We will apply this to the measurement of the charge exchange rate as described in Sec 4.5.

17

Chapter 3

Light Sources for Photoionization of Yb

In this chapter, we describe the light sources for ionizing Yb atoms. As we describe in Chap. 1, the photoionization scheme that we mainly investigate is the two-color excita-tion, where the1_S

01P1 transition in Yb atoms at 399 nm is driven as the rst-excitation

and Yb atoms in the 1_P

1 state are ionized by the second-excitation laser. For the

inves-tigations, we need a light source at 399 nm and another one for ionizing Yb atoms in the

1_P

1 state.

For the light source at 399 nm, a single-frequency continuous-wave (CW) tunable light source is desirable because this enables us to conduct isotope-selective loading by using the isotope shifts in the 1_S

01P1 transitions. We develop two light sources which satisfy

the requirement. One is a frequency-doubled titanium-sapphire laser (Ti:S) and the other is an extended cavity laser diode (ECLD).

The conversion eciency of the second-harmonic generation (SHG) of CW radiation in a nonlinear crystal is usually small. In order to enhance it, the nonlinear crystal is placed in an external cavity. We nd a problem when we maximize the enhancement factor, and demonstrate a solution to it, as shown in Sec. 3.2. Recently, diode lasers in the ultraviolet region are available. We can realize a compact tunable single-frequency light source by constructing an ECLD using one of those diode chips. We develop an ECLD at 399 nm using a high-output power diode chip which is very recently available. We describe the development in detail in Sec. 3.3 because the performance of the ECLD composed of a high-output power ultraviolet diode chip is not known. We also use other three ECLDs with low-power ultraviolet diode chips of dierent center wavelengths for the second ex-citation laser, although they are out of the scope of this thesis.

18 Chapter 3 Light Sources for Photoionization of Yb After we prepare the light sources, we next need to conduct frequency tuning of them. For the light source at 399 nm, a precise tuning is required for isotope-selective loading. Saturated absorption (SA) is one of the techniques used in high-resolution spectroscopy and is applied for the detection of the transitions in atoms and molecules used to obtain reference frequencies. Even after employing SA, isotope shifts and hyperne structures are sometimes incompletely resolved, and these unresolved lines contain signals of target iso-topes required for subsequent investigations. We demonstrate a simple method to detect minor isotope lines in SA by absorption ltering of major isotope lines. We investigate this method for the spectroscopy of the1_S

01P1 transition in Yb at 399 nm by controlling

the density of Yb atoms by varying the discharge current of a hollow cathode lamp.

3.1 Second Harmonic Generation of Titanium Sapphire Laser with

External Cavity Technique

The light source for driving the 1_S

0-1P1 transition at 399 nm, which we rst

de-veloped, is a frequency-doubled Ti:S laser. In order to generate CW ultraviolet light, SHG in nonlinear crystals has long been used. To increase the SH power, a nonlinear crystal is placed in an external cavity to enhance the fundamental power because of the low power of the beam from the CW laser [28]. Brewster-cut crystals [29,30] or antireec-tion (AR)-coated normal-cut crystals [31] are used as a nonlinear crystal in the external cavity. The former has the advantages that no loss is imposed by surface reection and that the astigmatism and coma introduced at the Brewster-cut facets are compensated by the folding angle of the concave mirrors to focus the beam in the crystal [32]. The latter is also widely used because it is easier to align the ring cavity and the aberrations are small provided the folding angle is small.

When the nesse of an external cavity is suciently high to obtain a large fundamen-tal enhancement factor, the enhancement factor, as described in the following section, is greatly aected by the round-trip loss. The small residual reection at the crystal facets is one of the main causes of this loss when a normal-cut crystal is used, even though the crystal facets are AR-coated. The reected beams from the two facets of the normal-cut crystal are subjected to interference, i.e., the crystal acts as an intracavity etalon. This

3.1 Second Harmonic Generation of Titanium Sapphire Laser with External Cavity Technique19 shows that the loss imposed by the residual reection at the crystal facets is eliminated

when the reected beams at the two facets are subjected to constructive interference. This technique is based on the theory of coupled cavity. Simultaneously, the interference causes the wavelength dependence of the enhancement factor, and the enhancement factor changes over long-time or day-to-day operation.

In this section, we discuss the eect of the small residual reection at the crystal facets on the enhancement factor and the wavelength dependence on the enhancement factor. To achieve constructive interference, i.e., the maximum enhancement factor at any wave-length, we demonstrate that temperature tuning is eective in our system containing a normal-cut β-BaB2O4 (BBO) crystal as a nonlinear crystal in an external cavity.

3.1.1 Eect of round-trip loss on enhancement factor

The fundamental enhancement factor A is described by A = 1− R

(1−√RV )2 , (3.1)

where R is the input mirror reectivity and the loss factor V is dened as V = 1 − L, where L is the fraction of the round-trip loss [28]. The linewidth of the fundamental laser is assumed to be narrower than the resonance width of the external cavity. Figure 3.1 shows the enhancement factor A as a function of the input mirror reectivity for various values of V . When the impedance matching condition, i.e., R = V , is satised, the maximum enhancement factor Amax = 1/(1− R) is achieved. Figure 3.2 depicts the Eq. (3.1) to

clarify the dependence of the enhancement factor A on V with the reectivity of the input mirror R as a parameter. When R is high, a small dierence in the intracavity loss markedly changes the enhancement factor. For example, for an external cavity with an input mirror of R = 0.99 and a fraction of round-trip loss of L = 0.008, one obtains A = 125. An increase in L of only 0.002, i.e., to 0.01, results in a decrease in A to 100. On the other hand, when R = 0.95, an increase in L of 0.002 only decreases A from 59 to 55. In addition, the SH power is proportional to the square of the enhancement factor. To achieve a high SH power by realizing a high enhancement factor using a high-reectivity input mirror, it is therefore essential to minimize the loss in the external cavity.

20 Chapter 3 Light Sources for Photoionization of Yb

0.90

0

0.92

0.94

0.96

0.98

1.00

50

100

150

Reflectivity of input mirror R

E

n

h

a

n

ce

m

e

n

t

fa

ct

o

r

A

V = .992

V = .990

V = .980

V = .970

Fig. 3.1 Calculated enhancement factor A as a function of the input mirror reec-tivity R with the loss factor V as a parameter, where V = 1 − L as L is the fraction of the round-trip loss. When the impedance matching condition, i.e., R = V is sat-ised, A is maximized for a given value of V . The thin line shows the maximum enhancement factor as a function of R. The two dots indicate the maximum and the minimum enhancement factor observed in our setup.

Eect of AR-coated facets of normal-cut nonlinear crystal

When one uses an AR-coated normal-cut nonlinear crystal in the external cavity, the residual reection at the crystal facets is one possible loss factor. However, it is possible to eliminate the loss imposed by the residual reection when the reected beams from the two facets are subjected to constructive interference, i.e., the intracavity etalon composed of the residual reection at the two crystal facets is resonant. The longitudinal mode spacing or free spectral range of a Fabry-Perot cavity in terms of wavelength ∆λ is given by

|∆λ| = λ2

2nl , (3.2)

where λ is the wavelength in vacuum, l is the distance between mirrors, and n is the refractive index of the material. We estimate ∆λ in our setup (see Sec. 3.1.2), which contains a 10-mm-long BBO crystal, to be 0.019 nm for a fundamental wavelength of λ = 798 nm, where n = 1.66 for ordinary light at 798 nm obtained from Sellmeier's

3.1 Second Harmonic Generation of Titanium Sapphire Laser with External Cavity Technique21

0.96

0

0.97

0.98

0.99

1.00

50

100

150

R = .990

R = .980

R = .950

R = .900

∼125

∼100

E

n

h

a

n

ce

me

n

t

fa

ct

o

r

A

Loss factor V

Fig. 3.2 Calculated enhancement factor A as a function of the loss factor V dened as V = 1 − L, where L is the fraction of the round-trip loss. When the reectivity of the input mirror R is high (> 0.98), the enhancement factor is strongly aected by the round-trip loss. For example, for R = 0.990, A decreases from 125 to 100 when

L increases only by 0.002 from 0.008 to 0.010.

equations described in Appendix A [33]. This shows that the enhancement factor, and hence the SH power, depends on the fundamental wavelength.

It is desirable to achieve the maximum enhancement factor at any wavelength. For this purpose, the interference caused by the residual reection at the two crystal facets must be tuned constructively. We investigate the temperature tuning of the optical path length of the cavity formed between the facets of the BBO crystal. In the worst case, temperature tuning is required to change the destructive interference to constructive interference. To realize this, the optical path length in the crystal is tuned by a quarter wavelength, with the change of the crystal temperature ∆T given by

d(nl) dT ∆T = (n dl dT + l dn dT)∆T = λ 4 , (3.3)

where T is the temperature of the crystal. We estimate ∆T for our BBO system. The thermo-optic coecient dn/dT for ordinary light is −16.6 × 10−6_{/K [34]. The thermal} expansion coecient, (1/l)dl/dT = 28×10−6_{/K at θ = 29.3}◦ _{of the phase-matching angle} of our target wavelength of 798 nm, is derived from the equation αasin2θ + αccos2θ [35]

22 Chapter 3 Light Sources for Photoionization of Yb Wave Meter PBS PZT

399 nm

OUTPUT

10 mm BBO

Fig. 3.3 Experimental setup. ISR, isolator; ML, mode-matching lens (f = 750 mm); M3, M4, concave mirrors with curvature radius of 50 mm; PZT, piezotransducer; PBS, polarizing beam splitter; PD, photodiode. The PD is used to monitor the fundamental power inside the external cavity.

and the known values of αa and αc of 4 × 10−6/K and 36 × 10−6/K, respectively [34].

We nd that a temperature change of 0.7 K is required to change the optical path length by λ/4 , i.e., to tune the enhancement factor from the minimum to the maximum. The temperature tuning of a BBO crystal in an external cavity has also been applied to tune the resonance frequency of the external cavity to enable frequency scanning of a laser system [36].

3.1.2 Experimental setup

Figure 3.3 shows a schematic diagram of the experimental setup. Radiation with a wavelength of 798 nm from a single-frequency CW titanium sapphire laser (Schwartz Electro-Optics Inc., Titan-CW). Two galvoplates and a galvo-driven thin etalon syn-chronously rotated with the galvoplates are introduced by us to enable frequency scan-ning.) is frequency doubled using a BBO crystal in an external cavity. The external cavity

3.1 Second Harmonic Generation of Titanium Sapphire Laser with External Cavity Technique23 is composed of four mirrors in a bow-tie conguration. The total cavity length is

approx-imately 400 mm, corresponding to a free spectral range of 750 MHz. The reectivity of the input mirror RM1 is 0.990 ± 0.002, and those of the other mirrors RM2, RM3, and RM4

are more than 0.998 for the fundamental wavelength of 798 nm. The transmissivity of the output mirror M4 is 0.95 at 399 nm. To focus the fundamental beam in the BBO crystal, we use two concave mirrors with a curvature of 50 mm. The resonance frequency of the external cavity is locked to the frequency of the laser by controlling the cavity length using a piezotransducer (PZT) on which M2 is mounted. The frequency deviation from the cavity resonance is detected by a polarization spectroscopic method [37].

The BBO crystal is cut to θ = 29.3◦ _{to achieve Type - I phase matching to the normal} incidence of the fundamental beam at 798 nm (Appendix A). The length of the crystal is 10 mm. The azimuth angle is cut to φ = 0◦ _{to maximize the nonlinear coecient. The input} and output facets are AR-coated for both fundamental and SH wavelengths. The BBO crystal is placed in a holder made of copper, which is mounted on a Peltier element. The temperature of the copper holder, measured using a thermistor, is temperature-controlled with a stability better than 0.01◦_{C (Thorlabs Inc., TED200C). Owing to the high nesse} of the external cavity, a beam reversely propagating in the cavity is built up and fed back to the laser. This prevents electronic locking of the cavity resonance to the laser frequency. To avoid optical feedback, we inserted two isolators (Isowave, I-80T-5M) with isolation above 35 dB.

3.1.3 Results and analysis

We measured the fundamental power built up in the external cavity and the SH power as a function of the fundamental wavelength, as shown in Fig. 3.4. We observed interference fringes in the fundamental power, and the SH power synchronously changed in propor-tional to the square of the fundamental power. The pitch of the fringes was measured to be 0.019 nm. This value was in agreement with that obtained in Sec. 3.1.1. Therefore, we conclude that the fringes observed in Fig. 3.4 are caused by the residual reection at the two facets of the BBO crystal.

We estimated the enhancement factor A by measuring the nesse of the external cavity. The nesse F is determined from the input mirror reectivity R and the round-trip loss

24 Chapter 3 Light Sources for Photoionization of Yb factor V by the following equation:

F = π(RV )1/4

1−√RV . (3.4)

One can determine the value of √RV, and then V , from the nesse F. Then, the enhancement factor A can be estimated from Eq. (3.1). We measured the nesse by linearly scanning the frequency of the Ti:S laser by rotating the galvoplates inside the laser cavity. The nesse was determined to be 350 for the constructive interference and 310 for the destructive interference. From the reectivity of the input mirror, RM 1 = 0.990 ± 0.002, the corresponding enhancement factors A was estimated to be 125 ± 25 and 100,± 20, and the ratios of the round trip loss L to be 0.008,± 0.002 and 0.010,± 0.002, respectively. The change in L shows that the residual reectivity at the AR-coated crystal facet is approximately 0.001 for each facet.

Figure 3.5 shows the fundamental and SH powers measured by changing the crystal temperature. We again observed the same periodic change in the enhancement factor as that shown as a function of the wavelength in Fig. 3.4 . The net optical path length nl in the crystal changed with its temperature and a temperature tuning of 3 K was required

0

20

40

60

80

100

797.820 797.840 797.860 797.880 797.900

R

e

la

tive

f

u

n

d

a

me

n

ta

l

p

o

w

e

r

/

a

.u

.

SH

p

o

w

e

r

/

mW

30

35

40

45

0.019 nm

Wavelength / nm

Fig. 3.4 Dependence of SH power (solid circles) and fundamental power (open dia-monds) on the fundamental wavelength. The dashed curve is a Fabry-Perot function tted to fundamental power. The solid curve is the square of the Fabry-Perot function tted to SH power.

3.1 Second Harmonic Generation of Titanium Sapphire Laser with External Cavity Technique25

20

40

60

80

100

20

30

40

50

30

35

40

45

SH

p

o

w

e

r

/

mW

R

e

la

tive

f

u

n

d

a

me

n

ta

l

p

o

w

e

r

/

a

.u

.

BBO temperature / ℃

3K

Fig. 3.5 Dependence of SH power (solid circles) and fundamental power (open dia-monds) on temperature of BBO crystal. The dashed curve is a Fabry-Perot function tted to the fundamental power. The solid curve is the square of the Fabry-Perot function tted to the SH power. The decrease due to phase-mismatching expressed as the square of the sinc function is also included in the tting.

to change the destructive interference to constructive interference, or a half cycle of the interference fringe in Fig. 3.5 . This result is dierent from the theoretical estimation of 0.7 K obtained in Sec. 3.1.1. The reason for the discrepancy is not yet known. Assuming that the thermooptic coecient is correct, we estimate the value of (1/l)dl/dT at 29.3◦ to be 14 × 10−6_/K.

When temperature-tuning the interference fringe, it is important that the phase-mismatching tolerance in SHG is much larger than the tuning temperature for each half cycle of the fringe. We dene the phase-mismatching tolerance as the full width at half maximum (FWHM) of a sinc function [sin(∆kl/2)/(∆kl/2)]2_{, where ∆k represents}

the phase mismatch. From the known parameters, we calculate the phase-mismatching tolerance to be 4.8 K as the estimation conducted in [34]. However, Fig. 3.5 shows that the eect of the phase-mismatching tolerance was negligible for tuning of 3 K. The observed phase-mismatching tolerance of approximately 50 K was much larger than the estimated value of 4.8 K. The discrepancy is caused by the fact that the interaction length is shorter than the crystal length owing to the double refraction in the BBO crystal [23].

26 Chapter 3 Light Sources for Photoionization of Yb The interaction length, i.e., the aperture length, expressed as la = π1/2ω0/ρ [38], was

calculated to be 0.6 mm in our case, where ρ is the walk-o angle as described below and in Appendix A. The FWHM phase-mismatching tolerance, derived using la instead of l, is 80 K. This is close to the experimental result.

We measured the day-to-day reproducibility of the SH power at a xed wavelength for one week; we switched the setup on and o every day but the crystal temperature was continuously controlled for one week. A uctuation of the SH power of 10 % was detected, while 40 % uctuation was observed in the day-to-day operation without temperature control owing to the uctuation of the ambient room temperature within approximately 2◦_C.

When we tune the optical path length in the crystal to produce constructive interfer-ence, the reection at the crystal facets is eliminated. Therefore, the backward beams in the external cavity, and hence the optical feedback to the laser, are minimized. We achieved electronic locking of the cavity resonance to the laser frequency using only one isolator because of the reduced optical feedback. When we changed the crystal temperature by 0.7 K from that resulting in constructive interference, we found that a second isolator was necessary for stable frequency locking. Each isolator has an insertion loss of 11 %. Therefore, the removal of one isolator has the benet of increasing the fundamental power and hence the SH power.

The method of temperature tuning to maximize the enhancement factor can be applied to an external cavity with other materials used as a nonlinear crystal. For example, with a 10 mm long normal-cut LBO crystal for SHG at 798 nm, we estimate that a temperature change of at most 0.3 K could maximize the enhancement factor according to our calculation for the BBO crystal. A dierent tuning method such as electronic tuning using an electrooptic eect may also be feasible.

SH power and conversion eciency

The SH power generated under constructive interference is plotted in Fig. 3.6 as a func-tion of the fundamental power. When the fundamental power in the crystal is depleted by conversion to the SH power and the absorption of the fundamental power and SH power in the crystal is negligible, the total conversion eciency γtotal= P2ω/Pω2, where Pω and

3.1 Second Harmonic Generation of Titanium Sapphire Laser with External Cavity Technique27 P2ω are fundamental power and SH power, respectively, is expressed as

γtotal = γSHGγmm2 A 2 = γ_mm2 A2 16π 2 ϵ0cλ3ω d2_el n2 h(B, ξ) , (3.5)

where γSHG is the single-path conversion eciency; γmm is the coupling or mode-matching

eciency of the fundamental beam to the external cavity; de is the eective nonlinear

coecient; ϵ0 is the electric constant; c is the vacuum speed of light; λω is the fundamental wavelength in vacuum; n is the refractive index, which is the same for the fundamental and SH powers upon phase matching; h(B, ξ) is the focusing function introduced by Boyd and Kleinman [38], where B is the double-refraction parameter dened as B = ρ(kωl)1/2/2, where ρ is the walk-o angle and kω is the propagation constant at the fundamental wavelength in the crystal; and ξ is the focusing parameter dened as ξ = l/b , where b = w₀2kω is the confocal parameter and w0 is the radius of the fundamental beam at focus.

0

100

200

300

400

0

50

100

150

SH

p

o

w

e

r

/

mW

Fundamental power / mW

0

10

20

30

40

Po

w

e

r-co

n

ve

rsi

o

n

e

ff

ici

e

n

cy

/

%

Fig. 3.6 SH power and corresponding power-conversion eciency P2ω/Pω as a

func-tion of the fundamental power when the fundamental enhancement factor is

maxi-mized by temperature tuning, where Pω and P2ωare the fundamental and SH powers,

respectively. The solid curve represents the calculated SH power assuming no deple-tion of the fundamental power by conversion to the SH power. The highest SH power of 125 mW was achieved at a fundamental power of 390 mW.

28 Chapter 3 Light Sources for Photoionization of Yb Our external cavity is designed so that ξ = 1.39. The walk-o angle ρ of 68 mrad (or 3.9◦₎ as described in Appendix A, leads to B = 12. Then, we estimate the value of h to be 0.058. We calculate de to be 1.9 pm/V from the equation de = d31sin(θ+ρ)+d22cos(θ+ρ) and

the known values of the coecients d31 and d22 of 0.04 pm/V and 2.3 pm/V, respectively

[39]. We estimate γSHG to be 0.93 × 10−4/W.We experimentally determined the value of

γmm to be 0.9. Finally, when we assume RM1 = 0.990, i.e., A = 125 for the constructive

interference, we estimate γtotal to be 1.2/W. This value is in good agreement with the

results shown in Fig. 3.6 in the region of low power-conversion eciency (P2ω/Pω) of below 15 %. The conversion eciency is similar to that obtained using a Brewster-cut BBO crystal [29,30]. The discrepancy compared with the estimated conversion eciency in the high power-conversion eciency region of over 15 % is caused by the depletion of the fundamental power by conversion to the SH power [40].

3.2 External Cavity Laser Diode 29

3.2 External Cavity Laser Diode

In order to realize a more compact and simple light source than the frequency-doubled Ti:S laser, we construct an ECLD with a high-power ultraviolet diode chip having a maximum output power of 100 mW (Nichia, 8C18KS). A diraction grating having 2400 grooves/mm and a blaze wavelength of 250 nm is placed in a Littrow conguration. The rst-order diracted beam whose power is 25% of the incident power is fed back to the chip, and the zeroth-order reection whose power is 64% of the incident power is produced as the output. The maximum power with which we achieve a single-frequency oscillation increases as the cavity length of the ECLD is shortened, as shown in Fig. 3.7. At the short-est cavity length of 14 mm, we obtain a tuning range with a single-frequency oscillation of 2 nm as shown in Fig. 3.8 and with a linewidth below 2 MHz and 20 MHz for observa-tion times of below 1 ms and 10 ms, respectively, as shown in Fig. 3.9. The linewidth is measured by beat signals at the frequency of the second harmonic of a titanium sapphire laser. The continuous frequency-tuning range of 3 GHz is achieved by scanning the voltage applied to a PZT which controls the cavity length.

Extended-cavity length / mm

M

a

xi

m

um

out

put

pow

e

r w

it

h

s

ingl

e

-fre

que

nc

y os

c

il

la

ti

on /

m

W

16

20

24

28

32

36

40

44

48

10

0

20

30

40

50

60

Fig. 3.7 Maximum output power achieved with single-frequency oscillation in ECLD with ultraviolet diode chip as a function of extended-cavity length.

30 Chapter 3 Light Sources for Photoionization of Yb 58 56 54 52 50 48 M a xi m um out put pow e r w it h si ngl e -fre que nc y os c il la ti on / m W 399.0 398.0 397.0 Current: 84 mA Wavelength / nm 398.5 397.5

Fig. 3.8 Wavelength dependence of output power at maximum operation current with single-frequency oscillation. Wavelength tuning is achieved over 2 nm at the maximum operation current by rotating the diraction grating.

3.2 External Cavity Laser Diode 31

Fig. 3.9 Beat signals between ECLD and frequency-doubled Ti:S laser. Linewidth with single-frequency oscillation is obtained to be 2 MHz (upper gure) and 20 MHz (lower gure) for observation times of below 1 ms and 10 ms, respectively. The observation times are estimated from the sweep times of the RF synthesizer.

32 Chapter 3 Light Sources for Photoionization of Yb

3.3 Saturated Absorption Spectroscopy of Yb Atoms in Hollow

Cathode Lamp

As we described in the introduction part of this chapter, precise frequency tuning is required in the light source at 399 nm, with which we drive the1_S

01P1 transition in Yb

as the rst-excitation for photoionization, in order to conduct isotope-selective loading. For this purpose, we detect saturated absorption (SA) signals of the transition. Saturated absorption is one of the techniques used in high-resolution spectroscopy and is applied to the detection of the transitions in atoms and molecules used to obtain reference fre-quencies. Even after employing SA, isotope shifts and hyperne structures are sometimes incompletely resolved, and these unresolved lines contain signals of target isotopes re-quired for subsequent investigations.

In this section, we describe a simple method to detect minor isotope lines in a SA spec-trum by absorption ltering of major isotope lines. We investigate this method for the spectroscopy of the 1_S

01P1 transition by controlling the density of Yb atoms by

vary-ing the discharge current of a hollow cathode lamp (HCL). As we described in Sec. 1.1,

171_Yb+ _{is an attractive isotope in optical frequency standards because it is insensitive to}

the magnetic eld. The natural abundance of the isotope 171 is small and 14%. Although, we develop this method for our future application to isotope-selective loading of Yb+_{, it}

can be applied to other transitions of other atoms which are intended to selectively detect the lines of their minor isotopes.

3.3.1 Principle of selective detection of minor isotope lines

We describe the principle of the selective detection. We assume that the intensity of a pump beam is greater than the saturation intensity at the entrance of the sample of atoms. As we increase the density of atoms, a signicant decrease in the pump beam intensity caused by linear absorption is observed, and nally, the pump beam intensity decreases below the saturation intensity before pump beam reaches the end of the sample. Under this condition, the probe beam, which enters the sample from the opposite side, is absorbed until it reaches the saturated part of the sample, i.e., we detect the SA signal

3.3 Saturated Absorption Spectroscopy of Yb Atoms in Hollow Cathode Lamp 33 using a probe beam with a lower intensity. On the other hand, the number of atoms that contribute to the SA signal does not increase as we further increase the density of atoms. The number of atoms that contribute to the SA signal increases at the entrance of the sample. However, the depth at which the pump beam intensity decreases below the saturation intensity is inversely proportional to the density of atoms. Therefore, when the depth at which the SA signal is generated is smaller than the sample length, the SA signal grows smaller as we further increase the density of atoms because the number of atoms that contribute to the SA signal, which is detected using the weakened probe beam by linear absorption, remains approximately constant. As we increase the density of atoms, the above phenomenon is rst observed in isotopes that have a high abundance and then in isotopes that have low abundance. Therefore, we can selectively detect the SA signal of minor isotopes by adjusting the appropriate density of the atoms.

We demonstrate this in a commercially available HCL by detecting the 1_S

01P1

tran-sition. This transition is used for not only the loading of Yb+ _{in an ion trap through}

photoionization but also the laser cooling of Yb [41]. The HCL is conveniently used to obtain the reference frequencies [42], and the density of the atoms is controlled by varying

PD

plate

Probe

plate

Pump

Fig. 3.10 Experimental setup of SA spectroscopy. PBS, polarizing beam splitter; PD, photodiode; ISR, isolator with isolation > 40 dB. The polarization of pump and probe lasers are tuned to be orthogonal each other by using the λ/2 plates.

34 Chapter 3 Light Sources for Photoionization of Yb the discharge current of the HCL.

3.3.2 Experimental setup and results

The experimental setup is shown in Fig. 3.10. The laser beam from the ECLD is split into a strong pump beam and a weak probe beam. The two beams are counterpropagated and overlapped in an HCL (Hamamatsu, L2783-70ANE-YB). The HCL contains a carrier gas comprising a mixture of Ar and Ne gases, which is injected into the HCL at pressures of 270 and 400 Pa. The powers of the pump and probe beams are 360 and 30 µW, respectively, at the window of the HCL. The scanning speed of the laser frequency is 15 MHz/s. To eliminate the component of linear absorption, the pump beam is chopped and the probe beam is detected at the chopping frequency by using a lock-in amplier. The typical chopping frequency is 1170 Hz.

The SA spectra are shown in Fig. 3.11 as a function of the discharge current of the HCL. The lines of the isotopes and the hyperne components are assigned by using the frequency intervals reported in the literature [43]. As described in Sec. 1.2, the natural abundance values of the Yb isotopes 176, 174, 173, 172, 171, 170, and 168 are 13, 32, 16, 22, 14, 3, and 0.1%, respectively. As the discharge current is increased, we rst observe that all the lines grow larger in proportion to the increase in the density of Yb atoms. Above a discharge current of 2 mA, the signals of the major isotopes 172 and 174 grow smaller, whereas the signal of the minor isotope 171 becomes more distinct, as discussed above. Because the lines of the two major isotopes are located around the center of the entire absorption structure, the lines at the edge of the structure for the isotopes 176, 171, 170, and 168 remain even at a high discharge current of more than 5 mA. At a high current of more than 5 mA, the probe beam is absorbed by the lines of the isotopes 176, 171, and 170, and nally, we observe only the signal of the isotope 168, which is the rarest isotope. We can set the optimum discharge current for each isotope to detect the SA signal with the highest resolution. For example, for the isotope 171, which is used as an optical frequency standard [2, 44], the discharge current of 2.02.8 mA gives us the best resolution.